ENGINEERING ETHICS ESI 6912
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This 2 page Class Notes was uploaded by Ms. Dorian Wiegand on Friday September 18, 2015. The Class Notes belongs to ESI 6912 at University of Florida taught by Stanislav Uryasev in Fall. Since its upload, it has received 15 views. For similar materials see /class/206804/esi-6912-university-of-florida in Industrial Engineering at University of Florida.
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Date Created: 09/18/15
Farming Example Extension Consider a European farmer who specializes in raising grain corn and sugar beets on his 500 acres of land During the winter he wants to decide how much land to devote to each crop The farmer knows that at least 200 T of wheat and 240 T of corn are needed for cattle feed These amounts can be raised on the farm or brought from a wholesaler Any production in excess of the feeding requirement will be sold Selling prices are 170 and 150 per ton of wheat and corn respectively The purchase prices are 40 more than this due to the wholesaler s margin and transportation costs Another pro table crop is sugar beet which sells at 36T however the European Commission imposes a quota on sugar beet production Any amount in excess of the quota can be sold only at 10 T The farmer s quota for next year is 6000T The yield on the land is a random variable This random variable is modeled by 6 year history of the land yields The data is given in the table of the Excel le assume that each scenario can happen with equal probability a Formulate and solve the SP problem using Excel LP solver b Compute 50CVaR and 50VaR for losses in optimal solution obtained in a c Minimize 50 CVaR ie nd the minimalrisk solution d Formulate and solve the SP problem using Excel LP solver given that 50 CVaR is less or equal 7000000 e Compute and compare 80 CVaR and 80 VaR for losses in optimal solutions obtained in a and in c f Minimize 80 CVaR and compare with 80 CVaR obtained in e Note Do not assume integrality of decision variables Formulation of Stochastic Programming Problem for the case of many scenarios p 150x1 230x2 260x3 238y15 210y25 l70w15 150w15 36w35 40m x1x2x3 3500 x1 20 stl y1 WI 2 200 W35 3 6000 Csx2 y25 wk 2 240 w 2 0 15253545 W3 WA S SBsxs y152535 Z 0 CVaR 1 S CVaRVR P VaR a S1 a S CVaR in constraint 1 S S 1 a 5 ZS Z PS VaR z 20 s VaR ZS S CVaR imaX 1 CVaR in objective min C VaR S CVaR VaRZzS 30 0 51 ZS Z Ps VaR ZS Z 0 PS 150x1 230x2 260x3 238y15 210y25 170w15 150w15 36w35 10WS x1x2x3 S500 x gt0 123 stl y15 WI 2 200 wk S 6000 Csxl yz WZS Z 240 W123s4 Z 0 W3 WA S SBsxs y152535 Z 0 1 S ZPS ZPimin S 51